In this paper, we employ BAR for variable selection problems in the illness-death model with semi-competing risks data. Furthermore, we assume data to be right-censored and potentially left-truncated data. The model we considered is the illness-death model studied by [1]}, [2]}, and [3]} under parametric and semiparametric model assumptions, respectively.
In the illness-death model, a shared frailty term is exploited to model the dependence among different events, and the Cox proportional hazards model is utilized to model three state transitions.
Depending on the knowledge of the baseline hazard functions in these transitions, we take two different approaches: parametric and semiparametric. We assume the Weibull baseline hazard functions in the parametric approach, where a standard parametric likelihood-based variable selection method can be formulated. In the semiparametric approach, we assume unknown baseline hazard functions and adopt the sieve method considered in [4]} to construct a penalized sieve likelihood for variable selection. Therefore, we approximate the baseline hazard functions by Bernstein polynomials that possess some significant advantages over similar methods. More discussion can be found in sec:discussion.
We propose an optimization algorithm that takes advantage of an iteratively reweighted least square method to implement the proposed method. This strategy approximates the likelihood function for a complicated model with a simple least squares function. An iterative optimization leads to a straightforward application of BAR in a simple linear model.
We evaluate the performance of the proposed variable selection method using BAR in extensive simulation studies and show its superior performance to other existing methods.
A generalized cross-validation (GCV) method is established for the tuning parameter selection. Finally, we apply our method to a colon cancer study for illustration.
